Incorporation of rapid association/dissociation processes in tissues into the monkey and human physiologically based pharmacokinetic models for manganese

Abstract In earlier physiologically based pharmacokinetic (PBPK) models for manganese (Mn), the kinetics of transport of Mn into and out of tissues were primarily driven by slow rates of association and dissociation of Mn with tissue binding sites. However, Mn is known to show rapidly reversible binding in tissues. An updated Mn model for primates, following similar work with rats, was developed that included rapid association/dissociation processes with tissue Mn-binding sites, accumulation of free Mn in tissues after saturation of these Mn-binding sites and rapid rates of entry into tissues. This alternative structure successfully described Mn kinetics in tissues in monkeys exposed to Mn via various routes including oral, inhalation, and intraperitoneal, subcutaneous, or intravenous injection and whole-body kinetics and tissue levels in humans. An important contribution of this effort is showing that the extension of the rate constants for binding and cellular uptake established in the monkey were also able to describe kinetic data from humans. With a consistent model structure for monkeys and humans, there is less need to rely on cadaver data and whole-body tracer studies alone to calibrate a human model. The increased biological relevance of the Mn model structure and parameters provides greater confidence in applying the Mn PBPK models to risk assessment. This model is also well-suited to explicitly incorporate emerging information on the role of transporters in tissue disposition, intestinal uptake, and hepatobiliary excretion of Mn.

Manganese (Mn) is an essential trace element found in all human tissues and is required for numerous physiological processes, including protein and carbohydrate metabolism, immune system function, and bone growth. When Mn intake exceeds elimination, Mn can accumulate in mid-brain regions that influence motor control, such as the globus pallidus, striatum, and substantia nigra (Dorman et al., 2006b;Yamada et al., 1986), resulting in neurotoxicity. Similar neurological responses have been linked to prolonged inhalation exposures (Pal et al., 1999) or ingestion of drinking water with high concentrations of Mn (Kawamura, 1941), or in patients with liver disease resulting in impaired Mn clearance (Spahr et al., 1996), and with long-term parenteral nutrition (Fell et al., 1996). For human risk assessment, it is important to determine the exposure conditions that result in Mn concentrations in the brain that are increased significantly compared with brain Mn concentrations arising from normal dietary intake (Andersen et al., 1999). Concerns surrounding chronic low-level Mn inhalation exposure have led to the development of an extensive Mn pharmacokinetic data set and physiologically based pharmacokinetic (PBPK) models for rats, monkeys, and humans Taylor et al., 2012). A series of pharmacokinetic approaches have been used to describe Mn kinetics, including compartmental models (Teeguarden et al., 2007a,b,c), PBPK models of adult rats, monkeys, and humans (Nong et al., 2008(Nong et al., , 2009Schroeter et al. 2011Schroeter et al. , 2012Yoon et al. 2019), and PBPK models of gestation and lactation in rats (Yoon et al., 2009a,b). The initial Mn compartmental PK models that relied on linear first-order processes to simulate Mn tissue kinetics under normal and deficient dietary conditions were unable to capture the rapid rise in tissue Mn concentrations seen during inhalation exposure to high Mn concentrations. A revised PBPK model structure was developed in the rat and monkey that allowed tissue compartments to maintain near constant Mn levels during normal dietary intake and included Mn tissue stores that could become saturated at higher exposures (Nong et al., 2009). Schroeter et al. (2011) extended the Nong et al. (2009) PBPK model for rats and monkeys to humans to predict inhalation exposure conditions expected to result in increased brain Mn concentrations in humans. This modeling effort included simulation of intravenous (iv), intraperitoneal (ip), and subcutaneous (sc) routes. This work also allowed for the analysis of studies of tracer kinetics of 54 Mn in monkeys and human volunteers as well as bulk Mn in tissues. These tracer studies with soluble carrier-free 54 Mn (given as 54 MnCl 2 ) reflect the overall kinetics of Mn in the body at different body burdens of Mn. Yoon et al. (2019) recast the PBPK model for the adult rat to have more rapid binding of Mn to and its dissociation from binding sites in tissues and more rapid tissue uptake. This effort was based on detailed understanding of the processes important to Mn homeostasis, including avid, rapidly reversible binding with multiple proteins/enzymes within tissues (Das et al., 2019;Wedler, 1993) and facilitated transport of Mn into and out of tissues via cellular Mn transporters (Aschner and Erikson, 2017;Chen et al., 2015). Several solute transporter proteins are involved in Mn homeostasis. In addition to divalent metal transporter 1 (DMT1), Zip-8 and transferrin/transferrin receptor system, SLC30A10, SLC39A8, and SLC39A14 are key transporters in Mn clearance and maintenance of Mn homeostasis in vertebrates (Chen et al., , 2015Leyva-Illades et al., 2014;Lin et al., 2017;Mercadante et al., 2019;Tuschl et al., 2016). Compared with Mn importers, an understanding of transporters for Mn efflux and the underlying mechanisms of Mn efflux and their role in maintaining Mn homeostasis in mammalian systems is more recent. SLC30A10 appears to be one of the more relevant Mn efflux transporters and plays a role in mediating Mn efflux in neuronal systems (Chen et al., 2015;Hutchens et al., 2017;Leyva-Illades et al., 2014).
In this study, a model structure with more rapid associationdissociation processes for Mn binding in tissues, first developed for the rat (Yoon et al. 2019), was extended to create similar PBPK model structures for monkey and human. These updated PBPK models more accurately represent the current state of the knowledge of Mn biology and will facilitate the incorporation of data from knowledge of Mn stores in tissues and the emerging information from both in vitro and in vivo studies on Mn transport. This more realistic PBPK model for Mn increases confidence in its use for human risk assessment.

PBPK model structure
This updated Mn PBPK model structure contains compartments for liver, lung, nasal cavity, bone, blood, cerebellum, olfactory bulb, globus pallidus, and pituitary gland (Figure 1). Physiological parameters for the monkey and human are reported in Table 1. An aggregated body tissue compartment represents all other tissues. The same model structure was used to examine data on Mn kinetics derived from studies with both monkeys and humans. The same kinetic data sets that were relied upon for this model had been employed in an earlier model that relied on a model structure with much slower association-dissociation processes (Schroeter et al., 2011. The manganese model presented here includes an expanded GI absorption description which can be adjusted to account for the dose-dependent uptake of orally administered manganese. This allows for simulation of concurrent exposure to dietary and inhaled Mn, and to simulate 54 Mn tracer kinetics from oral and inhalation exposure and from ip, iv, and sc dose routes. The inhalation exposure studies in monkeys that were relied upon for kinetic data sets were carried out with MnSO 4 particles, which are highly soluble in mucus and more rapidly taken up by the respiratory tract (Vitarella et al., 2000). The aerosol parameters for MnSO 4 consisted of a mass median aerodynamic diameter of 2.0 mm, a geometric standard deviation of 1.5, and a particle density of 2.95 g/cm 3 (Dorman et al., 2006a). The fractional deposition of inhaled MnSO 4 particles in the respiratory tract were calculated using the multiple-path particle dosimetry model (MPPD version 3.04; Anjilvel and Asgharian, 1995;Asgharian et al., 2001). Nasal deposition estimates from the MPPD model were partitioned onto the respiratory and olfactory epithelium based on species-dependent airflow allocation (Schroeter et al. 2011). Deposited Mn was assumed to be rapidly absorbed from lung tissues and nasal respiratory epithelium into the systemic circulation or transported from the nasal olfactory epithelium to the olfactory bulb.
GI absorption of Mn is dose dependent. GI absorption decreases and biliary excretion increases as dietary Mn levels increase (Dorman et al., 2006b;Teeguarden et al., 2007b). Previously established parameters including the fraction of Mn absorbed by the GI tract (FDIETUP) and the biliary excretion rate constant (KBILEC) were retained from the Schroeter et al. (2011) model, which had been calibrated based on steady-state tissue concentrations and 54 Mn whole-body elimination curves in monkeys. Induction of biliary elimination of Mn, which was included to describe increased bile elimination that was directly observed in higher exposure concentrations in monkeys (Nong et al., 2009), was retained in this effort. The biliary elimination rate was dependent on blood Mn concentration and followed a Michaelis-Menten pattern of induction: where KBILEX (l/h) is the rate of biliary excretion of Mn, KBILE is the allometrically scaled basal biliary excretion rate, KBINDUC, is the maximal increase in the biliary excretion rate, Cart is the concentration of Mn in the arterial blood, KM is the arterial concentration leading to half maximal induction, and n (parameter label is SLOPE in model file) is a Hill-type induction constant. The arterial blood concentration was used as a surrogate for free Mn liver concentrations, the presumed driver for Mn excretion, because Mn blood levels were directly measured in monkeys (Dorman et al., 2006a;Nong et al., 2009). We also modified the GI structure reported by Nong et al. (2009) to include fecal excretion in order to simulate the tracer kinetics of 54 Mn administered orally in monkeys and humans. To do this, a multicompartment gut was added to be consistent with the physiology of Mn absorption by the GI tract (Figure 1), following the approach of Schroeter et al. (2011). FDIETUP represents the fraction of dietary Mn absorbed from the GI tract and available to the systemic circulation. This process was described as a direct transfer from the gut lumen to the liver. The remaining fraction of Mn (1-FDIETUP) in the gut lumen is either retained in the gut in a gut tissue storage compartment representing enterocytes or directly transported to the lower GI tract lumen from which it is excreted in the feces. F ENT * K GI represents the storage rate constant into the enterocytes, where F ENT is the fraction stored and K GI is the rate constant for movement from the gut lumen. Mn transfer from the gut tissue storage compartment to the lower GI tract represents sloughing of the intestinal epithelial cells with a rate constant K ENT . This sloughed Mn is excreted in the feces without entering the systemic circulation. Mn elimination from the body in the feces was governed by the rate constant Tissue transport and binding model Transport and binding processes in Yoon et al. (2019) differed from those in the original Mn-PBPK models (Nong et al., 2009;Schroeter et al., 2011Schroeter et al., , 2012. In the earlier Mn PBPK models, the movement of Mn between the tissue and blood was relatively rapid while the association and dissociation rate of bound forms in tissue were slow and designed to be the limiting process for loss of Mn when body and tissue stores were reduced by alterations in intake or at the end of high dose exposures. In the revised Mn model (Figure 2) developed by Yoon et al. (2019), the binding and dissociation rate constants are much larger allowing tissue stores to adjust faster than was possible in the original model. The higher rates of tissue binding and the consistency of the dissociation equilibrium constant across tissues is more reflective of the biology of interactions of Mn with tissue proteins and tissue organelles (Das et al., 2019;Wedler, 1993). The use of a common dissociation constant (K D $ 0.5 lM) is also more consistent with similarities in Mn utilization and requirements across tissue types leading to the maintenance of Mn bound forms until the binding sites become saturated (Yoon et al. 2019). Variability in the presumed binding capacities across tissues still accounts for   Yoon et al. (2019). The K in and K out represent diffusion rate constants for Mn influx and efflux, respectively, whereas the k A and k D represent association and dissociation rate constants. Mn total is represented by MnFree plus MnBound, whereas Bmax (maximal binding capacity in a tissue) is represented by Bf (binding sites available for binding) plus MnBound.  Dorman et al. (2006a). Note: monkey cerebellum, olfactory bulb, and globus pallidus were calculated as 2 time's the right hemisphere volume as reported (see Supplementary Table 1 (Kepler et al., 1998). Significantly, a dose-dependent uptake process included in the globus pallidus and pituitary compartments in the earlier monkey models (Nong et al. 2009;Schroeter et al., 2011) was not required to reproduce the monkey data with the revised model. Parameter optimization for the monkey Mn transporter model was conducted to simultaneously estimate 3 parameters (KIN, KOUT, and BMAX) for each tissue. The cost function was based on minimization of the sum of squared error between the log model minus log data. The data sets used for optimization include the Dorman et al. (2006a) baseline diet values in all tissues (1st time-point in Figure 3A-J) and 1.5 mg/m 3 inhalation time-course data ( Figure 3A-J) and the whole-body clearance of 54 Mn studies (Dastur et al. 1971-ip;Furchner et al. 1966-iv and oral; Figure 4A-C). Parameters were estimated using the nloptr package (Ypma et al., 2020) which includes the derivation of the Subplex algorithm (NLOPT_LN_SBPLX) which is a variant of the Nelder-Mead algorithm. The final parameters are given in Table 2.

Human model parameterization
Physiological parameters in the human PBPK model were obtained from the literature (ICRP, 2002) ( Table 1). As noted previously, Mn dietary intake can vary widely and is typically between 1 and 10 mg/day (ATSDR, 2000). An average dietary intake of 3 mg/day Mn, and dietary absorption (FDIETUP) and biliary excretion (KBILEC) were retained from Schroeter et al. (2011). As was done with the monkey, the binding and dissociation rates were set to provide rapid binding kinetics. The remaining chemicalspecific parameters which had been optimized to the monkey kinetic studies (ie, tissue specific KIN, KOUT, and BMAX) were retained for simulation of the whole-body Mn clearance studies in humans.

Sensitivity analysis
A one-at-a-time (OAT) forward-difference sensitivity analysis was conducted to determine which model parameters had the greatest influence on the response variable. The sensitivity of all model parameters (excluding BW, QCC, and QPC) was assessed for the end of last exposure concentration in the globus pallidus. Both species were run with simulations assuming exposure for 90 days, with monkey and human exposed 6 h/day for 5 days/ week. Normalized sensitivity coefficients (fractional change in output divided by fractional change in input) were calculated. Normalization for the response variable and the parameter was included to allow a comparison across parameters and doses. The output was deemed sensitive to a parameter if the resulting coefficient was >0.1 in absolute value. Only parameters that were influential on at least one output metric are reported.

Monkey simulations
Simulation of the monkey studies used in the optimization of the influx and efflux rate constants and maximal binding capacities are shown in Figure 3A-J and Figure 4A-C. Overall, this recast Mn model provided reasonable fits to time-course tissue data ( Figure 3A-J). This comparison highlights the relatively flat response of visceral organs liver (3A), lung (3B), bone (3C), and muscle (3D) along with the measured bile (3E) and blood (3F) concentrations reported by Dorman et al. (2006a). At the same time, the model captures the rapid rise during the 90-day repeated exposures, as well as the rapid clearance after the last exposure in the brain target tissues (3G and 3I) where very discrete portions of the brain were sampled, as well as the pituitary (3H) and olfactory bulb (3J).  Figure 3. Simulated tissue Mn levels in monkeys exposed by inhalation to 1.5 mg Mn/m 3 for 90 days (6 h/day, 5 days/week). The simulation results are compared with data from Dorman et al. (2006a). The curves are model simulations and symbols are means from 4 to 6 monkeys per exposure concentration.
In Dastur et al. (1971), 12 rhesus monkeys with an average body weight of 2.5 kg were administered an ip dose of 200 mCi of carrier-free 54 MnCl 2 solution. Whole-body activity of 54 Mn was reported up to 278 days post-exposure. In keeping with the Schroeter et al. (2011) simulation of these data, the dietary intake was set to 80 ppm Mn, consistent with other published studies (Furchner et al., 1966), and the baseline dietary uptake (0.0002) was used. The updated Mn model captured the nonlinear dose-dependence of whole-body clearance of 54 Mn ( Figure 4A). The same correspondence was also the case for the Furchner et al. (1966) whole-body clearance studies with 54 MnCl 2 which included single monkeys administered 0.6 mCi 54 MnCl 2 as either an iv ( Figure 4B) or oral ( Figure 4C) bolus where the updated model provides an excellent representation of the data.
The optimized model was used to simulate the time-course fecal concentrations in monkeys after sc infusion (total infused: 200 mCi 54 Mn and 400 mg Mn in a MnCl 2 solution; Figure 5A) over 50 days and single exposure inhalation of nebulized 54 Mn (monkey A: 24 mCi; monkey B: 60 mCi; Figure 5B) reported by Newland et al. (1987). Both these dose routes were well described by the PBPK model without any alteration of the Mn kinetic parameters. The model performs well in capturing the steady-state wholebody tracer Mn achieved during the infusion ( Figure 5A) and, although there is some over-prediction of fecal concentrations during the clearance phase, the simulations provide a reasonable approximation of the shape of the clearance phase assuming approximately 50% of the dose was lost via necrosis of the skin reported at the pump injection sites. With these limitations, this result was considered a more qualitative simulation given the uncertainty in the administered dose in the sc study. Nonetheless, the simulation of the nebulized tracer Mn was accurately captured by the updated Mn model for monkey A, whereas monkey B, with the sc dosing, was only slightly underpredicted.  . Simulated whole-body retention of 54 Mn in monkeys compared with experimental data using of monkeys given a single dose of Mn via different exposure routes: (A) monkeys were exposed by ip injection to 200 mCi 54 MnCl 2 (Dastur et al., 1971); (B) monkeys were exposed by iv administration to 0.6 mCi 54 MnCl 2 (Furchner et al., 1966); (C) monkeys were orally dosed with 0.6 mCi of 54 MnCl 2 (Furchner et al., 1966). Curves represent the model simulations, and the symbols are retention data from individual monkeys.  provides very good fits to the concentration response across all tissues, capturing both the relatively flat response region and the more pronounced increases above about 0.1 mg/m 3 . In all tissues, the Mn model captured the changes in Mn disposition and clearance due to the increasing exposure concentration where saturation of tissue binding sites will be followed by marked increases in free Mn concentrations.

Human simulations
For the human modeling, the available data are primarily 54 Mn studies of whole-body retention (Figures 7-9) or changes in plasma concentration associated with changes in dietary intake ( Figure 10). As discussed previously, the parameterization for the human was primarily based on the monkey optimized parameters for maximal tissue binding, the rapid association/ Figure 7. Comparison of simulated whole-body retention in humans given an iv dose of 54 Mn with the whole-body retention data of Mahoney and Small (1968) and Mena et al. (1967). The curve represents the model simulation; the symbols for the Mahoney and Small (1968) study are retention data for individual subjects and the symbols for the Mena et al. (1967)     dissociation of tissue Mn binding, and more rapid transport into and out of tissues described for the adult rat Mn model (Yoon et al., 2019). Only the fraction uptake of dietary Mn and biliary excretion rate were estimated by fitting the model to the human data. All the model parameters reported by Schroeter et al. (2011) were retained in the human model. Figure 7 shows the comparison of simulated whole-body retention in humans given an iv dose of 54 Mn with the wholebody retention data of Mahoney and Small (1968) and Mena et al. (1967). The updated model provides an excellent fit to the initial whole-body retention of Mn up to 40 days post administration of the tracer Mn. Although the Mn model appeared to transition to a slower clearance phase somewhat earlier than seen in the data, the simulation was within a factor of 2 for both the Mahoney and Small (1968) and Mena et al. (1967) measured whole-body retention.
Simulation of the whole-body retention in subjects administered supplemental Mn (Mahoney and Small, 1968) is shown in Figure 8. The subject (J.M.) in Figure 8A was on a low-calorie diet and received about 1/3 of the daily intake of Mn prior to the iv administration of 54 Mn and for the first 60 days after tracer dosing. On day 60, the subject received daily supplementation of Mn (800 mg/day) for the remainder of the study. As with the Schroeter et al. (2011) model, to simulate the study results through 60 days, FDIETUP was increased from 0.06 to 0.062 and KBILEC was decreased from 0.051 to 0.02 l/h/BW 0.75 . On day 60 of the simulation, FDIETUP was returned to 0.06. Figure 8B shows the simulation of subject W.S. who was administered a daily supplemental oral dose of Mn (300 mg/day) starting 10 days prior to the iv administration of 54 Mn and was continued throughout the study. As described in Schroeter et al. (2011), FDIETUP was reduced each day for the first 15 days (ie, Àday 10 to þday 5). For our simulation, the best fit to the whole-body retention on Mn in subject W.S. was achieved with a daily reduction of 22% when compared with the 26% per day reduction in FDIETUP reported by Schroeter et al. (2011).
The whole-body retention of 54 Mn administered orally in a single meal (Davidsson et al. 1988) to 6 adult females is shown in Figure 9. As seen with the iv-tracer study, the simulations were generally consistent with data in 5 of the 6 subjects. One subject showed faster elimination of tracer and may have been on a diet with higher Mn levels than the other participants. The dashed curves in Figure 9 demonstrate the impact of a 3-fold opposed change in FDIETUP and KBILEC, to illustrate the influence of these 2 parameters on the whole-body clearance of 54 Mn. Overall, the current PBPK model simulations were consistent with results for all the data from human volunteers, capturing the clearance of orally administered tracer Mn over the 30-day simulation ( Figure 9) and with the iv-tracer study (Figure 7). The Mn model captured the transition from the rapid clearance phase to a slower phase seen at approximately 10 days-a result consistent with the Davidsson et al. (1988) retention data. Simulated plasma Mn concentrations ( Figure 10) were also compared with plasma Mn measurements from men consuming different levels of dietary Mn (Freeland-Graves, 1994). The updated Mn model successfully captured the change in plasma concentration associated with the change in dietary Mn intake and is an improvement over the simulations from Schroeter et al. (2011), who used a model with much slower association/dissociation rate constants for tissue binding of Mn. The simulations in Figure 10 did not require changing FDIETUP with changes in dietary Mn due to the small change in diet over the study.

Sensitivity analysis
OAT sensitivity coefficients for predicted globus pallidus concentration from a 1% change in model parameter values were determined at the end of 90 days (6 h/day, 5 days/week) for inhalation exposure concentrations of 0.01, 0.1, and 1.0 mg/m 3 Mn in monkeys and humans (Table 3). Model predictions were most sensitive to the influx and efflux diffusion rate constants (all parameters starting with "KIN" and "KOUT"). Model predictions were also sensitive to dietary absorption (FDIETUP and INFAC) and biliary elimination (KBILEC), although predictions became less sensitive with increasing inhalation exposure concentration as brain Mn levels were driven more by inhalation than diet. Sensitivity of model predictions displayed similar trends in monkeys and humans and were similar with sensitivity results in monkey and human reported in Schroeter et al. (2011) apart from the additional tissue transporter parameters (KINLIVC and KOUTLIVC) for liver that were added as part of Mn model refinement.

Kinetics of Mn interactions in tissues
The Schroeter et al. (2011) monkey and human Mn PBPK model structure was based on a particular set of assumptions and coherently integrated the state of the Mn biology at the time. As with these original models, the updated Mn model structure for the rat (Yoon et al., 2019) provided time profiles in the striatum after inhalation that were predominantly determined by increase in free Mn, with free tissue Mn expected to be responsible for Mn Table 3. Sensitivity analysis (one at a time a ) of peak Mn concentrations in the globus pallidus of monkeys and humans at inhalation concentrations of 0.01, 0. One at a time sensitivity coefficient was assessed using the forward difference with a delta of 1%. Coefficients were normalized to the parameter and endpoint to allow comparison across parameters and inhalation concentrations. Only parameters with at least 1 coefficient >0.1 were considered sensitive. Both monkey and human were exposed for 90 days, 6 h/ day, and 5 days/week. The globus pallidus concentration at the end of the last exposure was used in the calculation. toxicity. However, the processes that account for control of free Mn in tissues differ between these models. Yoon et al. (2019) updated Mn disposition in tissues with a description that is more consistent with current understanding of Mn biology. The dissociation equilibrium constant, K D , was a similar value across tissues, consistent with common biological functions of Mn irrespective of tissue/cell type. The K D used in the updated model (approximately 0.5 lM) reflected general binding affinity of Mn for multiple binding sites within tissues. To date there is little direct information to inform the amounts or affinity of the binding sites. Limited experimental evidence reports cellular free Mn in rat hepatocytes at around 0.2-1 lM based on electron paramagnetic resonance analysis (Ash and Schramm, 1982;Powell and Brew, 1976). Additionally, experimental studies report dissociation constants for Mn binding to galactosyltransferase and Mn 2þ -ATPase as 2.0 and 0.88 lM, respectively (Grisham and Mildvan, 1974;Powell and Brew, 1976). Our fitted dissociation rate constants, set at either 0.37 or 0.46 mM (20 or 25 mg/l) depending on the tissue, are in line with the estimated cellular concentration of free Mn and consistent with the K D from Yoon et al. (2019) and this literature. The dissociation rate constants, equivalent to half-lives of 4-5 min, are consistent with more readily interchangeable forms of cellular and subcellular forms of Mn. As in the earlier models, the binding capacity was set based on tissue concentrations measured in control animals or in human cadavers. The ability of the association/dissociation constants from the adult rat Mn model to represent the available data in the monkey is evidence that the primary binding depots are similar across mammalian species. Although the present model has much faster dissociation rate constants than used previously, these rate constants may not directly relate to dissociation of Mn from specific binding partners, such as Mnrequiring proteins throughout the cell. Rather they are likely to include both cytoplasmic protein partner dissociation rates and transport processes related to efflux of cellular Mn from subcellular organelles which also contain various metal ion transporters (Kambe et al., 2021). There remains uncertainty in the specific values of k A and K D . We found no literature reporting these kinetic constants and, due to the large number of binding partners, it would be difficult to generalize from results with any one protein to all other Mn-binding proteins. Upper bounds could be estimated by varying k D and k A to see what values would still fit the various data sets. No such exercise was attempted in this article.

Scaling to humans
The approach taken to extend the monkey model to the human in this effort differs from the approach used in Schroeter et al. (2011). In Schroeter et al. (2011) human model, some tissuespecific Mn parameters (KIN, KOUT, and BMAX) from the monkey were adjusted to provide better agreement with human cadaver tissue data and whole-body clearance studies resulting in increased uncertainty in the human model. For this updated monkey/human Mn model, only the uptake and clearance parameters, which are informed by the whole-body retention studies, were retained from the Schroeter et al. (2011) human model. The parameters associated with tissue binding and diffusion were scaled allometrically from the revised monkey model, which reflect the more rapid association/dissociation processes. With the success of this extrapolation in fitting the various human studies, the uncertainty in the Schroeter et al. (2011) human Mn model is significantly reduced because the parameters are now based on data that are informative of the ready availability of Mn among tissue stores. This result also supports the conclusion that the tissue disposition of Mn is conserved across species, with characteristics of the control of uptake of dietary Mn and biliary excretion accounting for many of the observed differences in whole-body uptake and clearance. The importance of control of dietary uptake and elimination are evident in fitting human tracer studies (Figure 9) where individual curves could be fitted by relatively small adjustments in uptake parameters for dietary Mn. Although there is no information on changes in human tissue levels with increasing exposures, the consistency of basal tissue levels across species and correspondence of altered whole-body clearance and increasing tissue levels in monkeys, provides high confidence that results from monkeys on tissue levels provide a good indication of conditions that will lead to similar increases in humans.

Parameter estimation
Compared with PBPK model development for the rat (Yoon et al., 2019), the equivalent monkey model was developed with more state-of-the-art curve fitting for the various data sets. With use of this more rigorous fitting approach, it was still necessary to include induction of the rate constant for biliary excretion with increases in exposure concentration and the induction parameters were used as described in Schroeter et al. (2011). Although biliary clearance was induced with increasing blood levels of Mn in the current monkey model, there was no need to retain the dose-dependent increase in brain region uptake as had been done in Schroeter et al. (2011). This difference in uptake processes, ie, inducible versus noninducible brain uptake, in the 2 monkey models may be due to the use of more formal fitting methods in the current modeling, together with inclusion of rapid association/dissociation processes that allow more rapid adjustments of tissue concentrations at initiation or cessation of exposures.

Uptake and clearance processes for cellular manganese
Although recasting the Mn PBPK models with rapid association and dissociation processes permits more rapid adjustment of tissue manganese with abrupt changes in oral or inhalation intakes (Yoon et al., 2019), these models still rely on fitting tissue uptake and elimination using input and efflux clearances (Table 2). Divalent metals are moved from blood into tissues and exit tissues to blood via transporters. They also move from the cytosol into subcellular organelles, each with differing requirements for the metal. Perhaps, the most well-characterized metal in relation to transporter proteins in cellular compartments is zinc (Kambe et al., 2021), where over 20 transporters have been described controlling uptake and efflux from blood into tissues and uptake and efflux from cytosol into subcellar organelles. These transporters fall into 2 broad categories, ZnT proteins and ZIP family proteins, with the former serving as efflux transporters and the latter as uptake transporters. The ZnT efflux proteins are members of the Slc30A1 through A10 family and the ZIP uptake proteins are in the Slc39A1 through Slc39A14 family. Inherited mutations in Slc30A10 (Quadri et al., 2012) and Slc39A14 (Tuschl et al., 2016) cause familial Mn neurotoxicity, and mutations in Slc39A8 cause low blood Mn concentrations, impaired glycosylation, and severe developmental abnormalities (Park et al., 2015). Clearly, these various transporter proteins have important functional roles in Mn homeostasis. These inherited mutations demonstrate both the high dose toxicity and essentiality based on the observation with loss of function of Slc39A8.
More detailed studies of the importance of Mn transporters in Mn toxicity have been accomplished using whole-body and tissue-specific knock-out mice with Slc30A10 and Slc39A14 (Mercadante et al., 2019). Whole-body knock-out of Slc39A10 led to accumulation of manganese in brain while pan-glial knockouts or the liver-specific knockout showed no significant tissue accumulation. Knocking out Slc30A10 in liver and enterocytes caused increased tissue Mn, but the increases were not as large as those seen with the global knock-out (Mercadante et al., 2019). Similarly, knock-out of Slc39A14 in liver did not lead to increases in tissue Mn as large as those seen with the whole-body knock out. At first glance, it seems paradoxical that increased tissue Mn occurs with loss of an efflux transporter (Slc30A10) and an uptake transporter (Slc39A14). However, the reason that loss of either causes Mn toxicity is likely associated with the roles of each transporter in biliary elimination of Mn. Net transport from blood to bile requires Slc39A14 transport from blood into hepatocytes and then efflux from hepatocytes to bile via Slc30A10 (Prajapati et al., 2021). The role of these and other transporters in uptake of Mn from the diet into enterocytes and efflux from enterocytes to blood is not as well-defined.
This rapid association-dissociation model for cellular Mn described here simply uses aggregated clearance terms for uptake into and efflux out of tissues without identifying specific molecular determinants of the movement. Nonetheless, for the purposes of Mn risk assessment, this model recapitulates conditions leading to brain accumulation of Mn in monkeys and characteristics of whole-body kinetics in humans and provides a basis for estimating the inhalation exposures that will cause significant increases in Mn in target areas of the brain. Because of the improved representation of Mn binding and movement compared with older modeling efforts (Nong et al., 2009;Schroeter et al., 2011), these newer model structures are more biologically realistic, but both the older models and the current model give similar results for the dose response of tissue accumulation and Mn intake. One clear difference in fitting time course Mn studies was the ability of the model, with more rapidly exchangeable tissue stores, to better represent whole body elimination of tracer 54 Mn after cessation of inhalation exposures at various concentrations (Yoon et al., 2019;Figs. 2 and 3).

Conclusion
PBPK models with more rapid association and dissociation kinetics of bound Mn better represent the known biochemistry of Mn compared with earlier models with much more slowly exchangeable Mn. This revised model structure was applied to describe dose dependencies of Mn in tissues of monkeys following inhalation exposures. The monkey model was also scaled to humans and was consistent with various human data sets evaluating clearance of tracer doses of 54 Mn. Despite the much improved fidelity with Mn biology of this revised model structure, both the older and newer PBPK models adequately described the dose dependence of increasing Mn concentration in various brain regions with increasing inhalation exposures or with increasing dietary intakes. Further mechanistic studies of Mn transporters, especially in regulating the dose dependencies in intestinal uptake and biliary excretion, should improve the correspondence between transporter properties and the fitted clearance terms that regulate tissue uptake, tissue efflux, and biliary excretion in the present models. Even absent further mechanistic development, the current PBPK models are well-suited for assisting in risk assessments of manganese.

Supplementary data
Supplementary data are available at Toxicological Sciences online.